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151-0709-00L 4 Credits BSC , MSC D-MAVT , D-INFK , D-MATH , D-CHAB

Stochastic Methods for Engineers and Natural Scientists

Lecturers & Examiners: PD Dr. Daniel Werner Meyer-Massetti

VVZ CR 3.67

Last Updated: 2026-06-03 00:07:34

Abstract

The course provides an introduction into stochastic methods that are applicable for the description, treatment, and modeling of systems that are subject to uncertainties or that respond to parameter changes in a chaotic manner. Corresponding systems may arise in fluid dynamics, structural mechanics, biology, electrical engineering as well as other areas.

Objective

By the end of the course you will be familiar with a range of mathematical/statistical tools that enable a quantitative treatment of problems that involve uncertainties.

Content

- Probability theory, single and multiple random variables, mappings of random variables - Estimation of statistical moments and probability densities based on data - Stochastic differential equations, Ito calculus, PDF evolution equations - Monte Carlo integration with importance and stratified sampling - Markov-chain Monte Carlo sampling - Control-variate and multi-level Monte Carlo estimation - Kalman filters (classical and ensemble-based) - Statistical tests for means and goodness-of-fit

Resources

Lecture Notes

Detailed lecture notes will be provided.

Literature

Some textbooks related to the material covered in the course: Stochastic Methods: A Handbook for the Natural and Social Sciences, Crispin Gardiner, Springer, 2010 The Fokker-Planck Equation: Methods of Solutions and Applications, Hannes Risken, Springer, 1996 Turbulent Flows, S.B. Pope, Cambridge University Press, 2000 Spectral Methods for Uncertainty Quantification, O.P. Le Maitre and O.M. Knio, Springer, 2010

General Information

Language: English
Levels: BSC , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 60 minutes
Aids: no aides are allowed

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Stochastic Methods for Engineers and Natural Scientists Lecture: 10-12 Exercises: 12-14	No time listed	4 h weekly

Offered In

Computational Science and Engineering Bachelor
- Fields of Specialization
  - Fluid Dynamics
Chemistry Bachelor
- Electives (Students are free to choose from a range of D-CHAB chemistry courses appropriate to their level of study (please note admission requirements). In case of doubt, contact the student administration.)
  - Computational Chemistry
Computer Science Bachelor
- Minor Courses
  - Minor Courses
Mechanical Engineering Master
- Core Courses (The Core Courses in the Master’s program Mechanical Engineering listed below are indicative and include courses designed by the Department at the Master's level. With the approval of the tutor, students may also select Master's-level courses offered by other departments at ETH. These courses will be marked as non-regular in the LAG, but their categorization as Core Courses is possible if included in the approved LAG.)
Computational Science and Engineering Master
- Fields of Specialization
  - Fluid Dynamics (One of the course units 151-0103-00L Fluid Dynamics II 151-0109-00L Turbulent Flows is compulsory. Students able to follow courses in German are advised to choose 151-0103-00L Fluid Dynamics II.)